The present invention relates to a method for estimating stable processing conditions in advance in order to prevent a self-excited cutting vibration which causes deterioration of a processing precision and breakage of a cutting tool in a case of processing a three-dimensional shape by a machine tool in which the cutting tool is moved while rotating the cutting tool.
In a cutting step by a rotary tool, relative vibrations of the tool and a work are sometimes generated due to low stiffness on a tool side or a work side or the like. The relative vibrations of the tool and the work are generated by a forced vibration or a self-excited vibration.
In the relative vibrations due to the former forced vibration, when a cutting edge of the rotary tool cuts through the work, a cutting force acts between the tool and the work, and a relative displacement is caused by this cutting force. In this case, the tool or the work vibrates at a cutting frequency determined by a product of the number of revolutions and the number of the cutting teeth of the tool. When the vibration (an amplitude) is large, a noise or a vibration of a processing machine is generated.
On the other hand, in the relative vibration due to the latter self-excited vibration, the vibration is generated in the vicinity of a natural frequency of a mechanical system such as the cutting tool, the machine tool or the work. The vibration has a characteristic that it does not start immediately after start of the cutting, but gradually increases as the cutting proceeds. In this case, the natural frequency of the mechanical system is generally several hundreds of hertz to several kilohertz in many cases. The noise due to the vibration has a comparatively high tone.
This self-excited vibration is modeled by a regenerative vibration theory proposed by Tlusty et al., and a technique to estimate the vibration in a numerical analysis manner is established. In this theory, an increase of the vibration of the tool during the cutting is referred to as a regeneration effect. Specifically, as shown in FIG. 2, this is a phenomenon in which the vibration of the tool is generated by a fluctuation of a chip thickness in a case where a wave surface formed by cutting the work with a cutting edge while vibrating in a previous period is cut by the next passing cutting edge, and the vibration increases as the cutting proceeds.
In FIG. 2, a chip thickness h(t) at a time t is represented by Equation (1):h(t)=h0−x(t−Δt)+x(t)  (1)in which Δt is a cutting period, x(t) is a displacement of the tool, and h0 is an initial chip thickness on processing conditions, that is, a tool feed amount per cutting tooth.
On the other hand, in a case where a motion of the tool is set to one degree of freedom as shown in FIG. 2, the motion of the tool is represented by the following equation:F=m{umlaut over (x)}+c{dot over (x)}+kx  (2)in which m is a mode mass, k is a spring constant, c is a decay constant, and F is an external force.
Moreover, the external force F of the above equation is a cutting force which acts between the tool and the work, and is represented by Equation (3):F=aKh(t)  (3)in which h(t) is the chip thickness, a is an axial depth of a cut (indicating an amount of the cut formed by the tool in a direction vertical to a drawing sheet surface in FIG. 2), and K is a proportionality factor determined by a combination of a tool geometry of the tool and a material to be cut.
Therefore, Equation (4) is derived using Equations (2) and (3).m{umlaut over (x)}+c{dot over (x)}+kx=aKh(t)  (4)
When a transfer function of a system represented by Equations (1) and (4) described above is evaluated and the stable axial depth a of the cut is mapped with respect to various cutting periods Δt, a curve is obtained as shown in FIG. 3. The cutting period can be converted into the number of the revolutions, if the number of the cutting teeth of the tool is known.
FIG. 3 shows a curve referred to as a stability limit curve. It is indicated that the depth of the cut larger than the depth shown by the curve is unstable, that is, the self-excited vibration is generated. In a case where this stability limit depth of the cut is estimated in advance to prepare an NC code, the NC code does not have to be adjusted afterwards due to the vibration generation, and the number of steps can largely be reduced.
In a document of Y. Altintas and E. Budak, 1995 Analytical Prediction of Stability Lobes in Milling Annals of the CIRP Vol. 44/1/1995: 357 to 362, a technique is developed in which a self-excited cutting vibration is regarded as a linear system to obtain the stability limit curve. According to the document, the stability limit curve can be obtained in a short time without repeatedly calculating any acceleration, speed or displacement that acts between the tool and the work corresponding to each of times in a time range.
However, the conventional self-excited cutting vibration analysis technique can only be applied to a case where a tool feeding direction is located in a plane vertical to a rotary shaft of the tool as in slotting in an XY-plane shown in FIG. 4. That is, the rotary shaft and the feeding direction of the tool, and an oblique angle of a processed surface are not considered. In actual component processing, for example, cutting of an oblique surface such as a wing surface of a fluid component shown in FIG. 6, the feeding direction of the tool may be not located in the plane vertical to the rotary shaft of the tool in some case.